A simple analogy will first be given which explains how repeated pressure fluctuations can induce vibration. FIG. 1 shows an acoustic loudspeaker 3 which produces pressure waves 6. Each wave 6 contains a high-pressure, high-density region 9, and a low-pressure, low-density region 12. When the waves 6 strike an object 15, each high-pressure region 9 applies a small force to the object 15, and the succeeding low-pressure region 12 relaxes the force. The sequence of. . . -force-relaxation-force-relaxation- . . .causes the object 15 to vibrate.
Shocks produced by rotating airfoils can produce similar vibrations, as will now be explained.
FIG. 2 illustrates a generalized shock 23 produced by a generalized airfoil 26. The shocks as drawn in FIG. 2, as well as in FIGS. 3 and 4, are not intended to be precise depictions, but are simplifications, to illustrate the principles under discussion.
One feature of the shock 23 is that the static pressure on side 29 is higher than that on side 32. Another feature is that the gas density on side 29 is higher than on side 32. These differentials in pressure and density can have deleterious effects, as will be explained with reference to FIGS. 3 and 4.
FIG. 3 illustrates a generalized gas turbine 35, which extracts energy from an incoming gas stream 38. Each blade 41 produces a shock 23A in FIG. 4 analogous to shock 23 in FIG. 2. The blades 41 in FIG. 4 collectively produce the shock system, or shock structure, 47.
Similar to the shock 23 in FIG. 2, each individual shock 23A in FIG. 4 is flanked by a differential in pressure and gas density: one side of the shock 23A is characterized by high pressure and high density; the other side is characterized by low pressure and low density.
When the shock structure 47 rotates, as it does in normal operation, it causes a sequence of pressure pulses to be applied to any stationary structure in the vicinity. This sequence of pulses is roughly analogous to the sequence of acoustic pressure waves 6 in FIG. 1.
For example, stationary guide vanes (not shown) are sometimes used to re-direct the gas streams exiting the blades 41 in FIGS. 3 and 4, in order to produce a more favorable angle-of-attack for blades on a downstream turbine (also not shown). The pulsating pressure and density pulses can generate vibration in the stationary guide vanes.
As a general principle, vibration in rotating machinery is to be avoided.
The preceding discussion is a simplification. In general, shocks 23A in FIG. 4 will be accompanied by expansion fans, and the overall aerodynamic structure will be quite complex. Nevertheless, the general principles explained above are still applicable.